Ashworth Semester Exam MA240 College Algebra

MA24S : College Algebra

Question 1
Solve the following equation. Determine whether the equation is an identity, conditional equation, or an inconsistent equation: 7(x - 4) = x + 2
{-7 ,conditional}
{7, Identity}
{5, conditional}
{2, inconsistent equation}

Question 2
Solve the following equation. Determine whether the equation is an identity, conditional equation, or an inconsistent equation: 7x + 13 = 2(2x - 5) + 3x + 23
Ø; conditional equation
Ø; Inconsistent equation
Ø; identity equation
{-1}; Inconsistent equation

Question 3
Determine the value of A so that the line whose equation is Ax + y - 2 = 0 is perpendicular to the line containing the points (1, -3) and (-2, 4).
– 3/7
5/9
–2/5
3/8

Question 4
Find the horizontal asymptote as x --> 8 and then describe what this means in practical terms. F(x) = 150x + 120/0.05x + 1; the number of bass, f(x), after x months in a lake that was stocked with 120 bass.
the number of bass, f(x), after y months in a lake that was stocked with 130 bass
the number of bass, f(x), after x months in a lake that was stocked with 120 bass
the number of bass, f(x), after x months in a lake that was stocked with 140 bass
the number of bass, f(x), after x months in a lake that was stocked with 150 bass

Question 5
Log4(3x+2) = 3
Solve the following logarithmic equation. Be sure to reject any value of x that is not in the domain of the original logarithmic expressions. Give the exact answer. Then, where necessary, use a calculator to obtain a decimal approximation, to two decimal places, for the solution:
{16/2}
{62/3}
{9/3}
{11/5}

Question 6
2x+5y = -2
3x-4y = 20
Solve the following system:
{(4, -1)}
{(1, -3)}
{(4, -2)}
{(1, -5)}

Question 7
x-2y+z=2
2x-y-z=1
Solve the following system of equations using matrices:
{(t, t 1, t)}
{(t, t 0, t)}
{(t, t - 2, t)}
{(t, t - 1, t)}

Question 8
3x+y-2z = -3
2x+7y+3z = 9
4x-3y-z = 7
Solve for x only using Cramer's Rule.
x = 7
x = 9
x = 2
x = -3

Question 9
X2 25 + (y-2)2 /36 = 1

For the following ellipses determine location of its foci.
foci at (0, 2 + v11), (0, 2 - v11)
foci at (0, 5 + v21), (0, 5 - v21)
foci at (0, 3 + v25), (0, 3 - v25)
foci at (0, 1 + v36), (0, 1 - v36)

Question 10
You are taking a multiple-choice test that has five questions. Each of the questions has three answer choices, with one correct answer per question. If you select one of these three choices for each question and leave nothing blank, in how many ways can you answer the questions?  
198 ways
290 ways
243 ways
364 ways

MA240 Module 7 Assignment - Probability

Assignment Instructions

M7 Assignment: Probability

Probability Report

The probability of an event can be determined in theory as well as in practice. In this project, you will use the formulas and methods in your readings to determine the theoretical probability. You will then conduct an experiment to see if the outcomes match what you expect to find with the theoretical probability.

 In this project you will:

1. be able to calculate and interpret probability
2. be able to analyze and compare theoretical and experimental probabilities

 To complete this project you will:

1. Complete the Probability Report Worksheet to guide you in writing your APA report. Be sure to show all work!

2. Complete a 2-page, double-spaced, APA-formatted report. In the report you need to present your findings and explain your conclusions on experimental and theoretical probability.  Thoughts to include in the report include: How are theoretical and experimental probability different? Why might the theoretical probability not match the experimental probability?
3. Be sure to cite your sources for the questions that require sources.

 

Probability Report Worksheet

 

Directions: Complete the probability report worksheet to help you with your calculations to create the APA report.



1. Choose one of the three scenarios:

a.       Probability of obtaining heads on a coin toss

b.      Probability of rolling a 2 on a 6-sided die.

c.       Probability of drawing a Jack from a deck of cards.

 

2. Calculate the theoretical probability for your chosen scenario. Show all work! Remember probability is the number of ways you can achieve the desired outcomes divided by the total number of outcomes.  Then calculate the theoretical probability of your chosen scenario NOT happening. Ex: What is the probability of "Not Heads"? What is the probability of "Not rolling a 2", etc.

3. Complete 100 trials for your chosen scenario. Example: Flip a coin 100 times and record the outcome, roll a die 100 times and record the outcome, choose a card from a deck (with replacement) 100 times.  


4. Create a table in Microsoft Word here and record your data.

5. Using the table you created in number 4, what is the experimental probability for your chosen scenario?

6. Using the table you created in number 4, what is the experimental probability for NOT achieving your chosen scenario? Example: What is the probability of "Not Heads"? What is the probability of "Not rolling a 2", and so on.

7. Does your theoretical probability match your experimental probability?

8. Complete research on WHY your probabilities might not match or why they might match. *Be sure to cite your source*

9. Using the concepts learned this week, what do you think would happen if you did 1,000 trials? *Be sure to cite your reading or lecture*

 

    

MA240 Assignment 4 M4 Assignment Financial Report

M4 Assignment: Financial Statement

Financial Report

Money is a central concept for everyone no matter what age you are. In this project, you will explore exponents using the compound interest formula to make conclusions on investments.  

In this project, you will:

1. Use exponents to calculate the amount of interest earned on an investment.
2. Evaluate formulas with exponents.
3. Convert interest rates to decimals.
4. Apply the order of operations.

 

To complete this project you will:

1. Complete the Financial Report Worksheet to guide you in developing your budget. Be sure to show all work!
2. Complete a 2-page, double-spaced, APA-formatted report. In the report, you need to present your findings and explain your conclusions on interest rates and compounding frequency. Thoughts to include in the report include: Is a savings account a good way to earn interest? When looking at opening a savings account, what should you look for: higher interest rate or more frequent compounding?
3. Be sure to cite your sources for the interest rates from the chosen financial institution!

 

Financial Report Worksheet

Directions: Complete the financial report worksheet to help you with your calculations to create the APA report.
1. Go to your financial institution's website or a local financial institution's website and find the interest rate and compounding frequency (monthly, quarterly, annually, and so on) for a savings account. Record that here:
2. Use the compound interest formula:  where r is the interest rate as a decimal, n is the number of times it is compounded in the time frame, t is the amount of time, and P is the starting value. Calculate your balance if you invest $1,000 for 1 year.

3. Using the compound interest formula, calculate your balance if you invest $1,000 for 5 years.

4. Now select a new compounding period (monthly, quarterly, annually, and so on) and redo your calculations from number 2 & 3, using the same interest rate.
5. Now select a new interest rate from another financial institution that is different than your starting one. Redo your calculations from numbers 2 & 3 with the new rate but keeping the same compounding frequency that you used in 2 & 3.

6. What did you learn about comparing the compounding frequency that interest is compounded?

7. What did you learn about comparing the interest rate?

8. Is it better to have a slightly higher rate or have interest compounded more often?

   

Ashworth Semester Exam - MA240 College Algebra

Question 1

Solve the following equation. Determine whether the equation is an identity, conditional equation, or an inconsistent equation: 7(x - 4) = x + 2

{-7 ,conditional}

{7, Identity}

 {5, conditional}

{2, inconsistent equation}

Question 2

Solve the following equation. Determine whether the equation is an identity, conditional equation, or an inconsistent equation: 7x + 13 = 2(2x - 5) + 3x + 23

Ø; conditional equation

Ø; Inconsistent equation

Ø; identity equation

{-1}; Inconsistent equation

Question 3

Determine the value of A so that the line whose equation is Ax + y - 2 = 0 is perpendicular to the line containing the points (1, -3) and (-2, 4).

– 3/7

5/9

–2/5

3/8

Question 4

Find the horizontal asymptote as x --> 8 and then describe what this means in practical terms. F(x) = 150x + 120/0.05x + 1; the number of bass, f(x), after x months in a lake that was stocked with 120 bass.

the number of bass, f(x), after y months in a lake that was stocked with 130 bass

the number of bass, f(x), after x months in a lake that was stocked with 120 bass

the number of bass, f(x), after x months in a lake that was stocked with 140 bass

the number of bass, f(x), after x months in a lake that was stocked with 150 bass

Question 5

 

Solve the following logarithmic equation. Be sure to reject any value of x that is not in the domain of the original logarithmic expressions. Give the exact answer. Then, where necessary, use a calculator to obtain a decimal approximation, to two decimal places, for the solution:

{16/2}

{62/3}

{9/3}

{11/5}

Question 6

 

Solve the following system:

{(4, -1)}

{(1, -3)}

{(4, -2)}

{(1, -5)}

Question 7

 

Solve the following system of equations using matrices:

{(t, t 1, t)}

{(t, t 0, t)}

{(t, t - 2, t)}

{(t, t - 1, t)}

Question 8

 

Solve for x only using Cramer's Rule.

x = 7

x = 9

x = 2

x = -3

Question 9

 

For the following ellipses determine location of its foci.

foci at (0, 2 + v11), (0, 2 - v11)

foci at (0, 5 + v21), (0, 5 - v21)

foci at (0, 3 + v25), (0, 3 - v25)

foci at (0, 1 + v36), (0, 1 - v36)

Question 10

You are taking a multiple-choice test that has five questions. Each of the questions has three answer choices, with one correct answer per question. If you select one of these three choices for each question and leave nothing blank, in how many ways can you answer the questions?

198 ways

290 ways

243 ways

364 ways

 

 

MA240 Online Exam 8_11 SCORE 100 PERCENT

Question 1 of 20

 

Write the first four terms of the following sequence whose general term is given.

a_n = 3n + 2

A. 4, 6, 10, 14

B. 6, 9, 12, 15

C. 5, 8, 11, 14

D. 7, 8, 12, 15

 

Question 2 of 20

 

If 20 people are selected at random, find the probability that at least 2 of them have the same birthday.

A. ≈ 0.31

B. ≈ 0.42

C. ≈ 0.45

D. ≈ 0.41

 

Question 3 of 20

 

You volunteer to help drive children at a charity event to the zoo, but you can fit only 8 of the 17 children present in your van. How many different groups of 8 children can you drive?

A. 32,317 groups

B. 23,330 groups

C. 24,310 groups

D. 25,410 groups

 

Question 4 of 20

 

Write the first four terms of the following sequence whose general term is given.

a_n = (-3)ⁿ

A. -4, 9, -25, 31

B. -5, 9, -27, 41

C. -2, 8, -17, 81

D. -3, 9, -27, 81

 

Question 5 of 20

 

k² + 3k + 2 = (k² + k) + 2 ( __________ )

A. k + 5

B. k + 1

C. k + 3

D. k + 2

 

Question 6 of 20

 

If two people are selected at random, the probability that they do not have the same birthday (day and month) is 365/365 * 364/365. (Ignore leap years and assume 365 days in a year.)

A. The first person can have any birthday in the year. The second person can have all but one birthday.

B. The second person can have any birthday in the year. The first person can have all but one birthday.

C. The first person cannot a birthday in the year. The second person can have all but one birthday.

D. The first person can have any birthday in the year. The second cannot have all but one birthday.

 

Question 7 of 20

 

Write the first six terms of the following arithmetic sequence.

a_n = a_n-1 - 10, a₁ = 30

A. 40, 30, 20, 0, -20, -10

B. 60, 40, 30, 0, -15, -10

C. 20, 10, 0, 0, -15, -20

D. 30, 20, 10, 0, -10, -20

 

Question 8 of 20

 

A club with ten members is to choose three officers—president, vice president, and secretary-treasurer. If each office is to be held by one person and no person can hold more than one office, in how many ways can those offices be filled?

A. 650 ways

B. 720 ways

C. 830 ways

D. 675 ways

 

Question 9 of 20

 

Use the Binomial Theorem to expand the following binomial and express the result in simplified form.

(2x³ - 1)⁴

A. 14x¹² - 22x⁹ + 14x⁶ - 6x³ + 1

B. 16x¹² - 32x⁹ + 24x⁶ - 8x³ + 1

C. 15x¹² - 16x⁹ + 34x⁶ - 10x³ + 1

D. 26x¹² - 42x⁹ + 34x⁶ - 18x³ + 1

 

Question 10 of 20

 

Write the first six terms of the following arithmetic sequence.

a₁ = 5/2, d = - ½

A. 3/2, 2, 1/2, 1, 1/4, 0

B. 7/2, 2, 5/2, 1 ,3/2, 0

C. 5/2, 2, 3/2, 1, 1/2, 0

D. 9/2, 2, 5/2, 1, 1/2, 0

 

Question 11 of 20

 

Write the first four terms of the following sequence whose general term is given.

a_n = 3ⁿ

A. 3, 9, 27, 81

B. 4, 10, 23, 91

C. 5, 9, 17, 31

D. 4, 10, 22, 41

 

Question 12 of 20

 

The following are defined using recursion formulas. Write the first four terms of each sequence.
 
a₁ = 4 and a_n = 2a_n-1 + 3 for n ≥ 2

A. 4, 15, 35, 453

B. 4, 11, 15, 13

C. 4, 11, 25, 53

D. 3, 19, 22, 53

 

Question 13 of 20

 

The following are defined using recursion formulas. Write the first four terms of each sequence.

a₁ = 3 and a_n = 4a_n-1 for n ≥ 2

A. 3, 12, 48, 192

B. 4, 11, 58, 92

C. 3, 14, 79, 123

D. 5, 14, 47, 177

 

Question 14 of 20

 

If three people are selected at random, find the probability that at least two of them have the same birthday.

A. ≈ 0.07

B. ≈ 0.02

C. ≈ 0.01

D. ≈ 0.001

 

Question 15 of 20

 

If three people are selected at random, find the probability that they all have different birthdays.

A. 365/365 * 365/364 * 363/365 ≈ 0.98

B. 365/364 * 364/365 * 363/364 ≈ 0.99

C. 365/365 * 365/363 * 363/365 ≈ 0.99

D. 365/365 * 364/365 * 363/365 ≈ 0.99

 

Question 16 of 20

 

Write a formula for the general term (the n^th term) of each arithmetic sequence. Do not use a recursion formula. Then use the formula for a_n to find a₂₀, the 20^th term of the sequence.

a_n = a_n-1 - 10, a₁ = 30

A. a_n = 60 - 10n; a = -260

B. a_n = 70 - 10n; a = -50

C. a_n = 40 - 10n; a = -160

D. a_n = 10 - 10n; a = -70

 

Question 17 of 20

 

Find the indicated term of the arithmetic sequence with first term, a₁, and common difference, d.

Find a₂₀₀ when a₁ = -40, d = 5

A. 865

B. 955

C. 678

D. 895

Question 18 of 20

 

Use the Binomial Theorem to find a polynomial expansion for the following function.

f₁(x) = (x - 2)⁴

A. f₁(x) = x⁴ - 5x³ + 14x² - 42x + 26

B. f₁(x) = x⁴ - 16x³ + 18x² - 22x + 18

C. f₁(x) = x⁴ - 18x³ + 24x² - 28x + 16

D. f₁(x) = x⁴ - 8x³ + 24x² - 32x + 16

 

Question 19 of 20

 

Find the indicated term of the arithmetic sequence with first term, a₁, and common difference, d.

Find a₅₀ when a₁ = 7, d = 5

A. 192

B. 252

C. 272

D. 287

 

Question 20 of 20

 

An election ballot asks voters to select three city commissioners from a group of six candidates. In how many ways can this be done?

A. 20 ways

B. 30 ways

C. 10 ways

D. 15 ways

 

   

MA240 Online Exam 7_10 SCORE 100 PERCENT

Question 1 of 40

5.0 Points

Solve the following system of equations using matrices. Use Gaussian elimination with back substitution or Gauss-Jordan elimination.

x + y + z = 4 x - y - z = 0 x - y + z = 2

 

A. {(3, 1, 0)}

B. {(2, 1, 1)}

C. {(4, 2, 1)}

D. {(2, 1, 0)}

 

Question 2 of 40

5.0 Points

Give the order of the following matrix; if A = [a_ij], identify a₃₂ and a₂₃.

1   0   -2

-5   7   1/2

∏   -6   11

e   -∏   -1/5

 

A. 3 * 4; a₃₂ = 1/45; a₂₃ = 6

B. 3 * 4; a₃₂ = 1/2; a₂₃ = -6

C. 3 * 2; a₃₂ = 1/3; a₂₃ = -5

D. 2 * 3; a₃₂ = 1/4; a₂₃ = 4

 

Question 3 of 40

5.0 Points

Use Gaussian elimination to find the complete solution to the following system of equations, or show that none exists.

3x + 4y + 2z = 3 4x - 2y - 8z = -4 x + y - z = 3

 

A. {(-2, 1, 2)}

B. {(-3, 4, -2)}

C. {(5, -4, -2)}

D. {(-2, 0, -1)}

 

Question 4 of 40

5.0 Points

Use Gaussian elimination to find the complete solution to each system.

x1 + 4x2 + 3x3 - 6x4 = 5 x1 + 3x2 + x3 - 4x4 = 3 2x1 + 8x2 + 7x3 - 5x4 = 11 2x1 + 5x2 - 6x4 = 4

 

A. {(-47t + 4, 12t, 7t + 1, t)}

B. {(-37t + 2, 16t, -7t + 1, t)}

C. {(-35t + 3, 16t, -6t + 1, t)}

D. {(-27t + 2, 17t, -7t + 1, t)}

 

Question 5 of 40

5.0 Points

Use Cramer's Rule to solve the following system.
 

x + 2y = 3 3x - 4y = 4

 

A. {(3, 1/5)}

B. {(5, 1/3)}

C. {(1, 1/2)}

D. {(2, 1/2)}

 

Question 6 of 40

5.0 Points

Use Gaussian elimination to find the complete solution to the following system of equations, or show that none exists.

w - 2x - y - 3z = -9 w + x - y = 0 3w + 4x + z = 6 2x - 2y + z = 3

 

A. {(-1, 2, 1, 1)}

B. {(-2, 2, 0, 1)}

C. {(0, 1, 1, 3)}

D. {(-1, 2, 1, 1)}

Question 7 of 40

5.0 Points

Use Gaussian elimination to find the complete solution to the following system of equations, or show that none exists.

8x + 5y + 11z = 30 -x - 4y + 2z = 3 2x - y + 5z = 12

 

• A. {(3 - 3t, 2 + t, t)}

B. {(6 - 3t, 2 + t, t)}

C. {(5 - 2t, -2 + t, t)}

D. {(2 - 1t, -4 + t, t)}

 

Question 8 of 40

5.0 Points

Use Cramer's Rule to solve the following system.

2x = 3y + 2 5x = 51 - 4y

 

A. {(8, 2)}

B. {(3, -4)}

C. {(2, 5)}

D. {(7, 4)}

 

Question 9 of 40

5.0 Points

Use Cramer's Rule to solve the following system.

x + 2y + 2z = 5 2x + 4y + 7z = 19 -2x - 5y - 2z = 8

 

A. {(33, -11, 4)}

B. {(13, 12, -3)}

C. {(23, -12, 3)}

D. {(13, -14, 3)}

 

 

 

Question 10 of 40

5.0 Points

If AB = -BA, then A and B are said to be anticommutative.

Are A =

0 1

-1 0

and B =

1 0

0   -1

anticommutative?

 

A. AB = -AB so they are not anticommutative.

B. AB = BA so they are anticommutative.

C. BA = -BA so they are not anticommutative.

D. AB = -BA so they are anticommutative.

 

Question 11 of 40

5.0 Points

Use Cramer's Rule to solve the following system.
 

12x + 3y = 15 2x - 3y = 13

 

A. {(2, -3)}

B. {(1, 3)}

C. {(3, -5)}

D. {(1, -7)}

 

Question 12 of 40

5.0 Points

Use Cramer's Rule to solve the following system.

x + y + z = 0 2x - y + z = -1 -x + 3y - z = -8

 

A. {(-1, -3, 7)}

B. {(-6, -2, 4)}

C. {(-5, -2, 7)}

D. {(-4, -1, 7)}

 

Question 13 of 40

5.0 Points

Use Gaussian elimination to find the complete solution to each system.

2x + 3y - 5z = 15 x + 2y - z = 4

 

A. {(6t + 28, -7t - 6, t)}

B. {(7t + 18, -3t - 7, t)}

C. {(7t + 19, -1t - 9, t)}

D. {(4t + 29, -3t - 2, t)}

 

Question 14 of 40

5.0 Points

Use Gaussian elimination to find the complete solution to each system.

x - 3y + z = 1 -2x + y + 3z = -7 x - 4y + 2z = 0

 

A. {(2t + 4, t + 1, t)}

B. {(2t + 5, t + 2, t)}

C. {(1t + 3, t + 2, t)}

D. {(3t + 3, t + 1, t)}

 

Question 15 of 40

5.0 Points

Use Cramer's Rule to solve the following system.
 

x + y = 7 x - y = 3

 

A. {(7, 2)}

B. {(8, -2)}

C. {(5, 2)}

D. {(9, 3)}

 

Question 16 of 40

5.0 Points

Solve the following system of equations using matrices. Use Gaussian elimination with back substitution or Gauss-Jordan elimination.

x - 2y + z = 0 y - 3z = -1 2y + 5z = -2

 

A. {(-1, -2, 0)}

B. {(-2, -1, 0)}

C. {(-5, -3, 0)}

D. {(-3, 0, 0)}

Question 17 of 40

5.0 Points

Solve the following system of equations using matrices. Use Gaussian elimination with back substitution or Gauss-Jordan elimination.

x + y - z = -2 2x - y + z = 5 -x + 2y + 2z = 1

 

A. {(0, -1, -2)}

B. {(2, 0, 2)}

C. {(1, -1, 2)}

D. {(4, -1, 3)}

Question 18 of 40

5.0 Points

Find the products AB and BA to determine whether B is the multiplicative inverse of A.

A =

0 0 1

1 0   0

0 1   0

 

B =

0 1 0

0 0   1

1 0   0

 

A. AB = I; BA = I₃; B = A

B. AB = I₃; BA = I₃; B = A^-1

C. AB = I; AB = I₃; B = A^-1

D. AB = I₃; BA = I₃; A = B^-1

 

Question 19 of 40

5.0 Points

Find values for x, y, and z so that the following matrices are equal.

2x z

y + 7 4

=

-10 6

13 4

 

A. x = -7; y = 6; z = 2

B. x = 5; y = -6; z = 2

C. x = -3; y = 4; z = 6

D. x = -5; y = 6; z = 6

 

Question 20 of 40

5.0 Points

Use Gauss-Jordan elimination to solve the system.

-x - y - z = 1 4x + 5y = 0 y - 3z = 0

 

A. {(14, -10, -3)}

B. {(10, -2, -6)}

C. {(15, -12, -4)}

D. {(11, -13, -4)}

Question 21 of 40

5.0 Points

Locate the foci of the ellipse of the following equation.
 
7x² = 35 - 5y²

A. Foci at (0, -√2) and (0, √2)

B. Foci at (0, -√1) and (0, √1)

C. Foci at (0, -√7) and (0, √7)

D. Foci at (0, -√5) and (0, √5)

 

Question 22 of 40

5.0 Points

Locate the foci and find the equations of the asymptotes.
 
x²/9 - y²/25 = 1

A. Foci: ({±√36, 0) ;asymptotes: y = ±5/3x

B. Foci: ({±√38, 0) ;asymptotes: y = ±5/3x

C. Foci: ({±√34, 0) ;asymptotes: y = ±5/3x

D. Foci: ({±√54, 0) ;asymptotes: y = ±6/3x

 

Question 23 of 40

5.0 Points

Find the vertex, focus, and directrix of each parabola with the given equation.

(x - 2)² = 8(y - 1)

A. Vertex: (3, 1); focus: (1, 3); directrix: y = -1

B. Vertex: (2, 1); focus: (2, 3); directrix: y = -1

C. Vertex: (1, 1); focus: (2, 4); directrix: y = -1

D. Vertex: (2, 3); focus: (4, 3); directrix: y = -1

 

Question 24 of 40

5.0 Points

Find the vertex, focus, and directrix of each parabola with the given equation.

(y + 1)² = -8x

A. Vertex: (0, -1); focus: (-2, -1); directrix: x = 2

B. Vertex: (0, -1); focus: (-3, -1); directrix: x = 3

C. Vertex: (0, -1); focus: (2, -1); directrix: x = 1

D. Vertex: (0, -3); focus: (-2, -1); directrix: x = 5

 

Question 25 of 40

5.0 Points

Locate the foci and find the equations of the asymptotes.
 
x²/100 - y²/64 = 1

A. Foci: ({= ±2√21, 0); asymptotes: y = ±2/5x

B. Foci: ({= ±2√31, 0); asymptotes: y = ±4/7x

C. Foci: ({= ±2√41, 0); asymptotes: y = ±4/7x

D. Foci: ({= ±2√41, 0); asymptotes: y = ±4/5x

 

Question 26 of 40

5.0 Points

Find the focus and directrix of each parabola with the given equation.

x² = -4y

A. Focus: (0, -1), directrix: y = 1

B. Focus: (0, -2), directrix: y = 1

C. Focus: (0, -4), directrix: y = 1

D. Focus: (0, -1), directrix: y = 2

 

Question 27 of 40

5.0 Points

Find the standard form of the equation of each hyperbola satisfying the given conditions.

Center: (4, -2)
Focus: (7, -2)
Vertex: (6, -2)

A. (x - 4)²/4 - (y + 2)²/5 = 1

B. (x - 4)²/7 - (y + 2)²/6 = 1

C. (x - 4)²/2 - (y + 2)²/6 = 1

D. (x - 4)²/3 - (y + 2)²/4 = 1

 

Question 28 of 40

5.0 Points

Find the standard form of the equation of the following ellipse satisfying the given conditions.

Foci: (-5, 0), (5, 0)
Vertices: (-8, 0), (8, 0)

A. x²/49 + y²/ 25 = 1

B. x²/64 + y²/39 = 1

C. x²/56 + y²/29 = 1

D. x²/36 + y²/27  = 1

 

Question 29 of 40

5.0 Points

Find the standard form of the equation of each hyperbola satisfying the given conditions.

Foci: (-4, 0), (4, 0)
Vertices: (-3, 0), (3, 0)

A. x²/4 - y²/6 = 1

B. x²/6 - y²/7 = 1

C. x²/6 - y²/7 = 1

D. x²/9 - y²/7 = 1

Question 30 of 40

5.0 Points

Locate the foci of the ellipse of the following equation.

25x² + 4y² = 100

A. Foci at (1, -√11) and (1, √11)

B. Foci at (0, -√25) and (0, √25)

C. Foci at (0, -√22) and (0, √22)

D. Foci at (0, -√21) and (0, √21)

 

Question 31 of 40

5.0 Points

Find the vertex, focus, and directrix of each parabola with the given equation.

(y + 3)² = 12(x + 1)

A. Vertex: (-1, -3); focus: (1, -3); directrix: x = -3

B. Vertex: (-1, -1); focus: (4, -3); directrix: x = -5

C. Vertex: (-2, -3); focus: (2, -4); directrix: x = -7

D. Vertex: (-1, -3); focus: (2, -3); directrix: x = -4

Question 32 of 40

5.0 Points

Find the solution set for each system by finding points of intersection.

x2 + y2 = 1 x2 + 9y = 9

 

A. {(0, -2), (0, 4)}

B. {(0, -2), (0, 1)}

C. {(0, -3), (0, 1)}

D. {(0, -1), (0, 1)}

 

Question 33 of 40

5.0 Points

Find the standard form of the equation of each hyperbola satisfying the given conditions.

Foci: (0, -3), (0, 3)
Vertices: (0, -1), (0, 1)

A. y² - x²/4 = 0

B. y² - x²/8 = 1

C. y² - x²/3 = 1

D. y² - x²/2 = 0

 

Question 34 of 40

5.0 Points

Find the vertices and locate the foci of each hyperbola with the given equation.

x²/4 - y²/1 =1

A.

Vertices at (2, 0) and (-2, 0); foci at (√5, 0) and (-√5, 0)

B.

Vertices at (3, 0) and (-3 0); foci at (12, 0) and (-12, 0)

C. Vertices at (4, 0) and (-4, 0); foci at (16, 0) and (-16, 0)

D. Vertices at (5, 0) and (-5, 0); foci at (11, 0) and (-11, 0)

 

Question 35 of 40

5.0 Points

Convert each equation to standard form by completing the square on x and y.

9x² + 25y² - 36x + 50y - 164 = 0

A. (x - 2)²/25 + (y + 1)²/9 = 1

B. (x - 2)²/24 + (y + 1)²/36 = 1

C. (x - 2)²/35 + (y + 1)²/25 = 1

D. (x - 2)²/22 + (y + 1)²/50 = 1

Question 36 of 40

5.0 Points

Locate the foci and find the equations of the asymptotes.
 
4y² – x² = 1

A. (0, ±√4/2); asymptotes: y = ±1/3x

B. (0, ±√5/2); asymptotes: y = ±1/2x

C. (0, ±√5/4); asymptotes: y = ±1/3x

D. (0, ±√5/3); asymptotes: y = ±1/2x

Question 37 of 40

5.0 Points

Find the vertices and locate the foci of each hyperbola with the given equation.

y²/4 - x²/1 = 1

A. Vertices at (0, 5) and (0, -5); foci at (0, 14) and (0, -14)

B. Vertices at (0, 6) and (0, -6); foci at (0, 13) and (0, -13)

C. Vertices at (0, 2) and (0, -2); foci at (0, √5) and (0, -√5)

D. Vertices at (0, 1) and (0, -1); foci at (0, 12) and (0, -12)

Question 38 of 40

5.0 Points

Convert each equation to standard form by completing the square on x and y.

9x² + 16y² - 18x + 64y - 71 = 0

A. (x - 1)²/9 + (y + 2)²/18 = 1

B. (x - 1)²/18 + (y + 2)²/71 = 1

C. (x - 1)²/16 + (y + 2)²/9 = 1

D. (x - 1)²/64 + (y + 2)²/9 = 1

Question 39 of 40

5.0 Points

Find the standard form of the equation of the following ellipse satisfying the given conditions.

Foci: (-2, 0), (2, 0)
Y-intercepts: -3 and 3

A. x²/23 + y²/6 = 1

B. x²/24 + y²/2 = 1

C. x²/13 + y²/9 = 1

D. x²/28 + y²/19 = 1

Question 40 of 40

5.0 Points

Find the standard form of the equation of the ellipse satisfying the given conditions.

Endpoints of major axis: (7, 9) and (7, 3)
Endpoints of minor axis: (5, 6) and (9, 6)

A. (x - 7)²/6 + (y - 6)²/7 = 1

B. (x - 7)²/5 + (y - 6)²/6 = 1

C. (x - 7)²/4 + (y - 6)²/9 = 1

D. (x - 5)²/4 + (y - 4)²/9 = 1